Disclosed is a supercharged direct-injection engine, which comprises a supercharging device (25, 30) for compressing intake air, and an injector 10 for directly injecting fuel into a combustion chamber 5. In the engine, an excess air factor λ as a ratio of an actual air-fuel ratio to a stoichiometric air-fuel ratio, at least in an engine warmed-up mode, is set to 2 or more in the entire engine-load region. Further, compressed self-ignited combustion is performed in a low engine-load region, and a supercharging amount by the supercharging device (25, 30) is increased along with an increase in engine load in a high engine-load region to allow the excess air factor λ to be kept at 2 or more. The engine of the present invention can effectively reduce NOx emission, while improving fuel economy.